In a bowl, toss the sliced flank steak with cornstarch until evenly coated. Let it sit for about 10 minutes to allow the cornstarch to adhere.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the beef in a single layer and cook for 2-3 minutes until browned. Flip and cook for an additional 2-3 minutes. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Add the minced garlic and ginger, and sauté for about 30 seconds until fragrant.
Pour in the soy sauce and brown sugar, stirring until the sugar dissolves. Bring the mixture to a simmer.
Return the beef to the skillet, tossing to coat it in the sauce. Cook for an additional 2-3 minutes until the sauce thickens slightly.
Stir in the chopped green onions and red pepper flakes, if using. Cook for another minute.
Serve the Mongolian beef over cooked rice.